In an isosceles triangle, the two equal sides are called legs, and the third side is called the base. The angle formed by the two equal sides is called the vertex angle. The other two angles are called base angles (Figure 1 ).

Isosceles triangles have at least two congruent sides and at least two congruent angles. The congruent sides, called legs, form the vertex angle. The other two congruent angles are the base angles.

VERTEX ANGLES

The two equal sides are called the legs and the third side is called the base of the triangle.

Little tick marks are used to show that two sides are the same length (congruent). You can use just one tick mark, two or three or more — just as long as you use the same number on sides that are equal.

A right triangle has one angle that’s 90° and a corner that looks like an L. Obtuse triangles have one angle that’s greater than 90°. In acute triangles, all the angles are less than 90°.

The sum of three angles of an isosceles triangle is always 180°, which means we can find out the third angle of a triangle if the two angles of an isosceles triangle are known.

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles. Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.

The converses of the Base Angles Theorem and the Isosceles Triangle Theorem are both true. Base Angles Theorem Converse: If two angles in a triangle are congruent, then the opposite sides are also congruent….Investigation: Isosceles Triangle Construction.